0

ACTIVATION ENERGY OF IODINATION OF ACETONE

Investigating the effect of temperature on the rate

of Iodination of Acetone, and hence determining

the Activation energy of the reaction.

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1 CONTENTS

Introduction: ........................................................................................................................................... 2

Research Question .................................................................................................................................. 5

Hypothesis............................................................................................................................................... 5

Variables ................................................................................................................................................. 5

Independent Variable ......................................................................................................................... 5

Dependent Variable ............................................................................................................................ 6

Controlled Variable ............................................................................................................................. 6

Apparatus ................................................................................................................................................ 8

Pre Lab Preparations ............................................................................................................................... 9

HCl (1.0 mol dm-3, 300 cm3) ............................................................................................................ 9

Acetone (4 mol dm3, 300 cm3) ........................................................................................................ 9

Iodine (0.005M, 300cm3) .............................................................................................................. 10

Procedure .............................................................................................................................................. 12

Setting up the apparatus .................................................................................................................. 12

Investigation procedure .................................................................................................................... 12

Safety Considerations ....................................................................................................................... 13

Data Collection and Processing ............................................................................................................. 14

Qualitative Data ................................................................................................................................ 14

Raw Data ........................................................................................................................................... 14

Data Processing ................................................................................................................................. 14

Conclusion and Evaluation .................................................................................................................... 22

Evaluation ......................................................................................................................................... 22

Error Evaluation ................................................................................................................................ 23

Further Investigation ............................................................................................................................ 24

Bibliography .......................................................................................................................................... 25

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2 INTRODUCTION

According to Chemical Kinetics, the rate of reaction, that is how fast a reaction occurs, depends on the concentration of reactants, the temperature, the presence of catalysts, the surface area of the reactants, and the solvents1. For any given reaction which is not reversible, the rate of reaction increases with the increase in temperature and concentration. To express the relation of rate of reaction with concentration of the reactants, the rate law is used. For a reaction:

xA + yB zC The rate can be expressed by the following equation2:

𝑟𝑎𝑡𝑒 = 𝑘[𝐴]𝑚[𝐵]𝑛 (1) Where: k is the rate constant [A] is the concentration of A in Moles per dm3 [B] is the concentration of B in Moles per dm3 m and n are the order of the reaction. As with the concentration, there is a relation between reaction rate and temperature. Temperature is the measure of the average kinetic energy of the molecules. The higher the Kinetic energy, the more the collisions taking place. While temperature affects the rate of the reaction, there is a certain minimum amount of energy required to initiate the reaction. This energy is called the Activation Energy. Activation energy can be defined as the minimum energy requirement that must be met for a chemical reaction to occur3.

Figure 1.1 – Graph of Total energy in the system against the progress of the reaction, representing the activation energy4.

1 http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Factors_That_Affect_Reaction_Rates 2 http://www.chm.davidson.edu/vce/Kinetics/DifferentialRateLaws.html 3http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Modeling_Reaction_Kinetics/Temperature_Dependence_of_Reaction_Rates/The_Arrhenius_Law/The_Arrhenius_Law%3A_Activation_Energies 4 http://courses.bio.indiana.edu/L104-Bonner/F13/imagesF13/L15/activation%20energy%20graph-01.jpg

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The equation relating the rate constant, k, to the temperature at which the reaction occurs, T, and the activation energy, Ea, is5:

𝑘 = 𝐴𝑒−(

𝐸𝑎𝑅𝑇

)

Where: k is the Rate Constant A is the frequency factor or the pre-exponential factor Ee is the Activation Energy at standard conditions R is the Universal Gas constant (8.314 joules mol-1 K-1) This equation is known as the Arrhenius Equation. The equation can be rewritten as:

ln(𝑘) = −𝐸𝑎

𝑅(

1

𝑇) + ln (𝐴)

This way, we get a straight line (y = mx + c) when we plot the graph of ln(k) vs 1/T. The slope of the equation will give us the activation energy. Thus, by measuring k at different temperatures we can determine graphically the activation energy for a reaction, as shown below: Figure 1.2 – An Arrhenius plot showing how Activation Energy is calculated. The graph is of the natural log of the Rate constant against the reciprocal value of the temperature of the reaction, in Kelvin6.

5 http://www.chem1.com/acad/webtext/dynamics/dynamics-3.html 6 http://www.chem.canterbury.ac.nz/LetsTalkChemistry/ElectronicVersion/ElectronicVersionNew/chapter16/arrhenius.shtml

(2)

4

The reaction taking place in the experiment is:

Figure 1.2 – Reaction of Acetone with Iodine

Picture taken from: http://mhchem.org/222/pdfLabs222/KineticsPartI.pdf

The rate of this reaction is expected to depend on the concentration of hydrogen ion in the solution, a catalyst, as well as the concentrations of the two reactants. By Equation 1, the rate law for this reaction is7:

𝑟𝑎𝑡𝑒 = 𝑘[𝑎𝑐𝑒𝑡𝑜𝑛𝑒]𝑚[𝐻+]𝑛[𝐼2]𝑝 (3) Where m, n, and p, are the orders of the reaction with respect to acetone, hydrogen ion, and iodine, respectively, and k is the rate constant for the reaction. It has been found that the rate is independent of the concentration of Iodine8. Thus, the values of m, n, p are found to be9: Table 1.1 – Values of ‘m’, ‘n’, ‘p’

Variable Value

m 1

n 1

p 0

The rate of this reaction can be expressed as the change in the concentration of I2, Δ[I2], divided by the time interval, Δt, required for the change10:

𝑟𝑎𝑡𝑒 =−∆[𝐼2]

∆𝑡 (4)

The minus sign is present because during the reaction, there is a reduction in the concentration of Iodine, and thus, the change is negative. This reaction was selected because from research, it is considerably slow so that the time of the reaction can be calculated with ease. Another characteristic of this reaction would be that reaction mixture would have a distinct pale yellow colour which can be easily observed visually. In this experiment, the reaction will be conducted at different temperatures the time taken for Iodine to completely react will be measured by observing the colour change. All further calculations will proceed as discussed further.

7,6 http://mhchem.org/222/pdfLabs222/KineticsPartI.pdf 8 It has been found that the rate of halogenation of acetone is independent of the concentration of halogen, except at very high acidities. http://www.tau.ac.il/~phchlab/experiments_new/kinetics/theory.html

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3 RESEARCH QUESTION

Investigating the effect of temperature on the rate of Iodination of Acetone, and hence determining

the Activation energy of the reaction.

4 HYPOTHESIS

According to kinetics, increasing the temperature and providing heat energy increases the rate of

reaction by speeding up the molecular collisions in a reaction. Thus, increasing the temperature in

this reaction would reduce the time taken to complete the reaction. Not much can be concluded

about the Activation Energy of the reaction, except the fact that it would be negative, as the slope of

ln(k) vs. RT is a negative slope. Also, there is no literature value available of the Activation Energy of

this particular reaction at Standard Conditions.

5 VARIABLES

5.1 INDEPENDENT VARIABLE

Variable Unit How it was measured

Temperature of the reaction

mixture

˚C ±0.05 This parameter was changed and controlled using a water bath. The decided temperature range was from 25˚C to 45˚C, at intervals of 5˚C, the only reason being that 25˚C was the room temperature, and reducing the temperature further would be difficult and would require a different apparatus; and increasing the temperature above 45˚C would increase the rate of the reaction, which would make it difficult to measure the time accurately.

The apparatus for the following was a water bath of heated water, in which the reaction container was dipped until the desired temperature was reached, and then adding the final reactant, Acetone, to the mixture. The temperature inside was continuously logged using the Pasco Spark Data Logger, and in the event of any decrease in temperature, the reaction container was briefly dipped in the water bath. During an event of an increase in temperature, the reaction container was dipped in another beaker of cool water in order to maintain the temperature.

This method of maintaining a constant temperature is systematically not precise, but within the given limits of the lab apparatus, it was the only reasonable option. The detailed error analysis of the process is done further.

The least count of the data logger and temperature probe was 0.1˚C, making the error ±0.05˚C

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5.2 DEPENDENT VARIABLE

Variable Unit How it was measured

Time of reaction

Seconds (s) ±0.005 The time was measured using a stopwatch. The least count of the stopwatch is 0.01 seconds, and thus, the uncertainty is ±0.005 s

For each value of temperature, five similar trials were conducted. The time for each was noted down, and an average of the five values was considered to be the final time of the reaction. This way, any random errors in the experiment might be reduced.

5.3 CONTROLLED VARIABLE

Variable Unit How it was controlled

Concentration of the

reactants

mol dm-3 The concentration of the reactants in the reaction mixture was kept constant, as only the effect of temperature on the rate of reaction was of importance. Varying the concentration would also change the rate of the reaction. Therefore, the following constant concentrations were decided upon:

Table 3.1 – Initial concentrations of the reactants

Initial Concentrations (mol dm-3)

HCl Acetone I2

1 4 0.005

These values were maintained by making the reactants manually, with utmost care. For measuring the concentration, first, a solution of a known concentration was taken, or a solid form of the reactant was taken (wherever appropriate); to which appropriate amount of water was added in order to obtain the desired concentrations.

The solutions from which the reactants were made, are assumed to have no errors. The uncertainty in the produced concentrations is discussed further in Preparation of Reagents

Volume of each reactant

cm3 Volume of each reactant in the reaction mixture was kept constant, to ensure that for each trial, the same amount of reactant is reacting with the other. This is essential in ensuring that temperature is the only factor causing a change in the rate. The volumes of the reactants were kept as follows:

Table 3.2 – Volumes of the reactants used in the reaction.

HCl (cm3) Acetone (cm3) I2 (cm3) Water (cm3)

10 10 10 20

Note: Water is not a reactant, but it varies the concentration of the other reactants, and hence, the amount of water was also constant.

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These volumes were measured using a 10 cm3 measuring cylinder which has a least count of 0.1 cm3 and, and therefore, the uncertainty in each reactant is - ±0.05 cm3 for HCl, ±0.05 cm3 for Acetone, ±0.05 cm3 for I2, and ±0.1 cm3 for water, as it was measured out twice.

Total volume of the reaction

mixture

cm3 The total volume of the reaction mixture was kept constant at 50 cm3. The reactants were added in fixed amounts like mentioned above, into the main reaction container.

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6 APPARATUS

Table 5.1 – Apparatus used in the investigation

Apparatus Capacity Uncertainty Quantity

Glass beakers 50 cm3 - 4

Glass beaker 500 cm3 - 1

Conical flask 200 cm3 - 1

Measuring cylinder 10 cm3 ± 0.1 cm3 4

Measuring cylinder 50 cm3 ± 0.5 cm3 1

Measuring cylinder 500 cm3 - 1

Bunsen Burner - - 1

Tripod Stand - - 1

Wire Mesh - - 1

Label stickers - - 1

Stopwatch - - 1

Magnetic stirrer - - 1

White paper sheet - - 1

Airtight bottles >300 cm3 - 2

Dropper - - 1

Glass rod - - 1

Digital balance - - 1

Pasco Spark Data Logger

- - 1

Spark Temperature probe (DS18B20)

- - 1

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7 PRE LAB PREPARATIONS

7.1.1 HCl (1.0 mol dm-3, 300 cm3)

Preparation

1. Concentrated HCl of 12.0 mol dm-3 concentration was used as initial solution.

2. Using equation

𝑀1𝑉1 = 𝑀2𝑉2

M1 = 12 mol dm-3

M2 = 1.0 mol dm-3

V2 = 0.3 dm3

𝑉1 =1 ×0.3

12 = 0.025 dm3 = 25 cm3

3. Take 25 cm3 of 5.0 M HCl in a 50 cm3 measuring cylinder

4. Pour the HCl in a 500 cm3 measuring cylinder and add distilled water to it until the whole

solution becomes 300 cm3. (Distilled water amount added should be (300-25) cm3 = 275 cm3

5. Add the solution in the beaker and stir it using a clean and dry glass rod

6. Using an aluminium foil, cover the beaker, in order to avoid evaporation of HCl

Uncertainty

The error in measuring volume in Step 4 is ±0.5 cm3, as the least count of the measuring cylinder is 1

cm3. The error in measuring volume of water in step 5 is ±2.5 cm3, as the least count of the 500 cm3

measuring cylinder is 5 cm3.

Therefore, the total error in measuring the volume is

±(0.5 + 2.5)cm3 = ±3cm3 = ± 0.003 dm3

Thus, the concentration is 1.0 ± 0.003 M

7.1.2 Acetone (4 mol dm3, 300 cm3)

Calculations

Mr of Acetone = 58.08 g mol-1.

Table 6.2.1 – Calculations for mass of Acetone required to prepare 300 cm3 of 4 mol dm-3 of Acetone solution.

Mass of Acetone (g) Volume of Acetone Solution (dm3) Concentration (mol dm3)

58.08 1 1

58.08 x 4 = 232.23 1 1 x 4 = 4

232.23 x 0.3 1 x 0.3 4

69.669 0.3 4

Therefore, the required mass of Acetone in grams is 69.669 grams.

Density of Acetone (STP) = 0.790 g cm-3

Volume = 𝑀𝑎𝑠𝑠

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 69.669/0.790 = 88.1886 ≈ 88.2 cm3

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Preparation

1. Measure 88 cm3 Acetone in a 100 cm3 measuring cylinder

2. Pour the Acetone into a 500 cm3 measuring cylinder

3. Add distilled water to the 500 cm3 measuring cylinder until the solution becomes 300 cm3 in

total. (Amount of distilled water added should be about (300-88) cm3 = 212 cm3)

4. Pour out the contents of the 500 cm3 measuring cylinder into a clean, airtight chemical

container.

Uncertainty

The uncertainty in step 1 is ±0.5 cm3 as the least count of the measuring cylinder is 1.0 cm3. The

uncertainty in step 4 is ±2.5 cm3 as the least count of the measuring cylinder is 5.0 cm3.

Therefore, the total uncertainty in volume = ±(0.5 + 2.5) cm3 = ±3.0 cm3 = 0.003 dm3

Therefore, the uncertainty in Concentration is 4 ± 0.003 mol dm-3

7.1.3 Iodine (0.005M, 300cm3)

Calculations

Molar Mass of I2 = 253.81

Concentration required = 0.005 mol dm-3

𝑀𝑎𝑠𝑠 = 𝑀𝑜𝑙𝑒𝑠 × 𝑀𝑜𝑙𝑎𝑟 𝑀𝑎𝑠𝑠

𝑀𝑎𝑠𝑠 = 0.005 × 253.81 = 1.269 𝑔𝑟𝑎𝑚𝑠

Therefore, 1.269 grams of I2 will yield 1 dm3 of 0.005M solution.

Thus, for 200cm3 of solution:

(1.269 𝑔𝑟𝑎𝑚𝑠 ×200 𝑐𝑚3

1000 𝑐𝑚3) = 0.2538 = 0.254 𝑔𝑟𝑎𝑚𝑠

Preparation

1. Measure 300cm3 concentrated Potassium Iodide (KI) in a washed and dry 500cm3 measuring

cylinder, and pour it in a clean beaker.

2. Measure 0.254 grams of Iodine granules on a digital balance as accurately as possible

3. Take the Iodine granules and add it to the KI solution

4. With a glass rod, stir the solution until the granules are not visible. If the Iodine is taking a

long time to dissolve, crush the pellets with the glass rod and put the beaker over a magnetic

stirrer, and start the process.

5. After a few minutes, the granules should disappear and should impart a dark maroon colour

to the solution.

6. Cover the beaker with a plastic or aluminium foil to prevent any impurities from falling in.

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Uncertainty

The uncertainty in measuring volume in the first step is ±2.5 cm3, as the least count of a 500cm3

measuring cylinder is 5 cm3

The uncertainty in measuring the mass in Step 2 is ±0.0005g as the least count of the digital balance

is 0.001g

Thus, the total uncertainty in Moles is ±0.0005 mol because moles is nothing but the mass divided by

the molar mass.

The uncertainty in volume is ±2.5cm3 that is ±0.0025dm3

Therefore, the Total Percentage uncertainty:

(2.5

300× 100) + (

0.0005

0.005× 100) = 10.008%

Therefore, the absolute uncertainty is

10.008

100× 0.005 𝑚𝑜𝑙 𝑑𝑚−3 ≈ 0.0005 𝑚𝑜𝑙 𝑑𝑚−3

The final concentration of I2 solution is 0.005 ± 0.0005 M

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8 PROCEDURE

8.1 SETTING UP THE APPARATUS 1. Take the individual beakers of the reagents and label them according to their contents.

2. Place them in a line, and in front of each one of them, for the sake of convenience, place a

10cm3 measuring cylinder which is cleaned and dry.

3. Fill a 500cm3 beaker with approximately 300cm3 distilled water and place it next to the

beakers with its own 10cm3 measuring cylinder.

4. Besides the chemicals, place a 1000 cm3 glass beaker filled with approximately 400 cm3 of

water, on a wire mesh over a tripod stand.

5. Place a Bunsen burner under the stand

6. Take a dry and cleaned 200 cm3 conical flask, which will be our reaction container, and place

the temperature probe inside such that the tip touches the base of the conical flask. Lead

the remaining wire out of the flask

7. Keep a cork ready next to the flask as on adding the reactants, the cork will have to be

fastened on the flask.

8. Place a piece of white paper next to the setup, which will be used to compare the colour.

8.2 INVESTIGATION PROCEDURE Table 7.1 – Volumes of the reactants to be taken in the procedure, and the temperature for each trial

Trial Volumes of reactants

Total Volume (cm3) Temperature (˚C) ± 0.05˚C

HCl (cm3) ± 0.1 cm3

Acetone (cm3) ± 0.1 cm3

I2 (cm3) ± 0.1 cm3

Water (cm3) ± 0.2 cm3

1 10 10 10 20 50 25

2 10 10 10 20 50 30

3 10 10 10 20 50 35

4 10 10 10 20 50 40

5 10 10 10 20 50 45

1. Switch on the Bunsen burner

2. Set up a new experiment on the data logger and start logging the temperature

3. Measure and add 10 cm3 of HCl in the reaction container.

4. Add 20 cm3 of water after measuring it in the measuring cylinder, into the reaction

container.

5. To this, add 10 cm3 of Iodine solution

6. Make sure the temperature probe inside is dipped in the liquid.

7. Fasten the reaction container with the cork

8. Using a test tube holder, dip the flask in the water bath

9. Keep the container in the water until the temperature required is reached. You will have to

keep an eye on the data logger simultaneously.

10. When the temperature required is reached, quickly remove the flask from the water bath

and let the temperature come to the required amount.

11. When the required temperature is attained, uncork the flask, add 10 cm3 of Acetone to it,

and then cork it again as fast as you can. Start the stopwatch simultaneously.

12. There should be a small drop in the temperature, and to heat up the reaction again, dip the

container in the water bath for a short time, until the temperature required is reached.

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13. Remove the container from the water bath again, and keep swirling it with your hand until

the colour of the contents becomes transparent. Use the white sheet of paper to compare

the colour.

14. If there is a drop in the temperature, dip it in the water bath again for a short time, to reach

the desired temperature. Under rare circumstances, if there is cooling required, pour some

cold water over the flask to maintain the temperature.

15. At the point the solution becomes transparent, stop the stopwatch.

16. Record the time in a table.

17. Clean the reaction container properly and dry it with a cloth, and prepare it for the next run.

Repeat Steps 3 to 17 five times for each trial, recording your results in a table given below.

Table 7.2 – Observation Table to record the results.

Trial No.

Temperature (˚C) ± 0.005

Time Taken (s) ±0.005s

T1 T2 T3 T4 T5

1 25

2 30

3 35

4 40

5 45

8.3 SAFETY CONSIDERATIONS Handle HCl with care, especially concentrated HCl, while making the reactant.

Do not touch Iodine pellets directly with your hand. Use a spatula.

Do not try to inhale over Iodine solution or Acetone, as both form vapours, though Iodine

takes time.

While the experiment is going on, wear a lab coat, safety goggles, and gloves at all times.

Do not touch the Bunsen burner, tripod stand, or the wire mesh at any time in the

experiment, as they are extremely hot.

Always dip the reaction container gently in the water bath to avoid splashes.

Conduct the experiment under adult supervision.

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9 DATA COLLECTION AND PROCESSING

9.1 QUALITATIVE DATA On adding Iodine to the reaction mixture, the solution turns pale yellow. After the addition of

Acetone, the solution slowly starts to lose the colour and becomes colourless. This is a considerably

slow reaction and requires patience. The time taken to turn colourless starts decreasing as the

temperature increases.

9.2 RAW DATA The following table illustrates the readings obtained on conducting the investigation.

Table 8.2 – Readings from the investigation

Trial No. Temperature

(˚C) ± 0.005

Time Taken (s) ±0.005s

T1 T2 T3 T4 T5

1 25 174.90 175.38 172.46 175.27 176.15

2 30 102.32 101.49 99.68 103.76 102.16

3 35 61.88 59.15 60.53 62.71 59.89

4 40 36.60 36.42 35.92 37.43 37.78

5 45 25.5 26.78 24.96 25.48 23.75

9.3 DATA PROCESSING Of the readings shown in Table 6.1, an average of the values was taken for each of the trials.

Trial 1:

174.9 + 175.38 + 172.46 + 175.27 + 176.15

5 = 174.832 ≈ 174.83 𝑠

Uncertainty:

The uncertainty of this average value can be calculated by calculating the standard deviation in the

values.

The standard deviation in values is given by the formula11:

𝜎 = √∑ (𝑥𝑖 − 𝑥𝑎𝑣𝑔)2𝑛

𝑖=1

𝑛

Therefore,

𝜎 = √(174.9 − 174.83)2 + (175.38 − 174.83)2 + (172.46 − 174.83)2 + (175.27 − 174.83)2 + (176.15 − 174.83)2

5

𝜎 = ±1.40𝑠

Similarly, the process was repeated for the other trials. The results are shown below.

11 https://www.mathsisfun.com/data/standard-deviation-formulas.html

15

Table 8.3.1 – Average of the readings for each trial

Trial Tavg (s) Standard Deviation (s)

1 174.83 ± 1.40

2 101.88 ± 1.48

3 60.83 ± 1.45

4 36.83 ± 0.76

5 25.29 ± 1.09

Next, the actual concentration of each reagent in the reaction mixture was calculated.

Sample calculation for Trial 1:

HCl Initial Concentration (M1) = 1 ± 0.003 mol dm-3

HCl Initial Volume (V1) = 10 ± 0.1 cm3

Total Volume (V2) = 50 ± (0.1+0.1+0.1+0.1) cm3 = 50 ± 0.4 cm3

Therefore, HCl Final Concentration (M2) = M1V1/V2

(1 ± 0.003 𝑚𝑜𝑙 𝑑𝑚−3) × (10 ± 0.1 𝑚𝐿)

(50 ± 0.4 𝑚𝐿)=

(1 ± 0.3%) × (10 ± 1%)

(50 ± 0.8%)= 0.2 ± 1.1%

= 0.2 ± 0.0022 𝑚𝑜𝑙 𝑑𝑚−3

Similarly, the final concentration, which is the concentration of each reactant in the reaction mixture

was calculated similarly. The results are shown in the table below.

Table 8.3.2 – Initial Volumes, Initial Concentrations, Final Volumes, and Final Concentrations of all the reactants. Note: The Final Volume is same as the Total Volume.

Initial Volumes (cm3)

HCl (± 0.1 cm3)

Acetone (± 0.1 cm3)

I2

(± 0.1 cm3) Water

(± 0.1 cm3) Total Volume

(± 0.4 cm3)

10 10 10 20 25

Initial Concentrations (M)

HCl (± 0.003 mol dm-3)

Acetone (± 0.003 mol dm-3)

I2

(± 0.0005 mol dm-3)

1.000 4.000 0.005

Final Concentrations (M)

HCl (± 0.0022 mol dm-3)

Acetone (± 0.015 mol dm-3)

I2

(± 0.0001 mol dm-3)

0.200 0.800 0.001

The next step is to find inverse of the Temperature, as the Arrhenius plot requires the value of T-1 to

be on the x-axis. To find this, we first need to convert the temperature from Celsius scale to Kelvin.

For this, the value 273 has to be added to the Celsius reading.

For example, for 25˚C, its conversion to Kelvin would be (25 + 273) K = 298 K

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This was done for all the temperatures used in the experiment. The results are shown in the table

below:

Table 8.3.4 – Temperatures in Kelvin from Celsius scale

Temperature (˚C) Temperature (K)

25 ± 0.05 298 ± 0.05

30 ± 0.05 303 ± 0.05

35 ± 0.05 308 ± 0.05

40 ± 0.05 313 ± 0.05

45 ± 0.05 318 ± 0.05

To find T-1, we need to find the inverse of all the Kelvin values.

For example, for the value of 298 K, the inverse would be 1

298 = 0.003355705

The Uncertainty of these inverse values would have the same percentage uncertainty. Therefore:

Percentage uncertainty of Trial 1:

0.05

298× 100 = 0.01677% ≈ 0.017%

Since the uncertainty is almost negligible in the temperature readings, it has been ignored

throughout.

Similarly, the inverse value for all Temperature values were found:

Table 8.3.5 – Inverse of the Temperature values in Kelvin

Temperature (K) Temperature-1 (K-1)

298 ± 0.05 0.003355705

303 ± 0.05 0.003300330

308 ± 0.05 0.003246753

313 ± 0.05 0.003194888

318 ± 0.05 0.003144654

The next step is to calculate the rate of the reaction. As we know, the rate of the reaction can be

expressed as the change in concentration of the reactant, divided by the time taken for reaction. In

this investigation, we are looking at the rate of reaction with respect to Iodine, as we are sure that

the Iodine is reacting completely from the Qualitative data observation. Thus, we know that the rate

of change of concentration of Iodine is same as the Final Concentration of Iodine for a trial (Table

7.2) because all of the Iodine is reacting. Therefore, the equation becomes:

𝑟𝑎𝑡𝑒 =∆[𝐼2]

𝑡𝑎𝑣𝑔

Sample Calculation of Rate for Trial 1:

(0.001

174.83) = 5.71978 × 10−6 𝑚𝑜𝑙 𝑑𝑚−3𝑠−1

Similarly, the rate of reaction of each trial was calculated.

17

For calculating the uncertainty in rate, the percentage uncertainties in the concentration of Iodine

and time are added.

Uncertainty in [I2] = 10.008% (From Pre-Lab Preparation of Iodine)

Uncertainty in Time = 1.40

174.83× 100 = 0.8% (From Table 7.1)

Total Percentage Uncertainty = (10.008 + 0.8)% = 10.808%

The process was carried on for all the readings.

The results are shown in the table below.

The graph of Rate of the Reaction vs. Temperature is shown below:

Figure 8.3.1 – The Graph of Rate of Reaction against the Temperature. This graph is discussed

in the Conclusion and Evaluation section. The points marked in red are also discussed later.

0.000000

0.000005

0.000010

0.000015

0.000020

0.000025

0.000030

0.000035

0.000040

0.000045

0.000050

295 300 305 310 315 320

Rat

e o

f re

acti

on

(m

ol d

m-3

s-1)

Temprature (K) ±0.05

Rate of Reaction vs Temperature

Table 8.3.6 – Rate of reaction for each trial

Trial Temperature (˚C) Rate (mol dm-3 s⁻1) Percentage Uncertainty (%)

1 25 5.71978 x 10-6 10.808

2 30 9.81528 x 10-6 11.461

3 35 1.64387 x 10-6 12.392

4 40 2.71518 x 10-5 12.072

5 45 3.95351 x 10-5 14.318

18

The next step is calculating the rate constant (k), as the y-axis of the Arrhenius plot is natural log of k.

To calculate k, we need to know the Rate of the reaction, the concentrations of the reactants of non-

zero order, and the orders of the reaction. The order of reaction of the reactants were found in

another experiment. The orders are summarized in the table below:

Table 8.3.7 – Values of ‘m’, ‘n’, ‘p’, where ‘m’ is the order of Acetone, ‘n’ is the order of H+ ion, and

‘p’ is the order of I2.

Variable Value

m 1

n 1

p 0

Now that we know the order of the reactions with respect to all the reactants, we can calculate the

rate constant (k), using the rate law.

Sample calculation for Trial 1:

𝑅𝑎𝑡𝑒1 = 𝑘[𝐴𝑐𝑒𝑡𝑜𝑛𝑒]1[𝐻+]1[𝐼2]0

(5.71978 × 10−6) = 𝑘(0.8)1(0.2)1(0.001)0

𝑘 =(5.71978 × 10−6 )

{(0.8)(0.2)}

𝑘 = 3.57486 × 10−5 𝑚𝑜𝑙−1𝑑𝑚3 𝑠−1

Uncertainty in Rate Constant:

𝑘 =(5.71978 × 10−6 ± 10.808%)

(0.8 ± 1.875%)(0.2 ± 1.100%)

∆𝑘 = 10.808 + 1.875 + 1.100 = 13.783%

∴ 𝑘 = 3.57486 × 10−5 ± 13.783% 𝑚𝑜𝑙−1𝑑𝑚3 𝑠−1

Similarly, the calculations were repeated for all the trials. The results are displayed in the table

below.

Table 8.3.8 – Values of rate constant (k) for each trial

Trial K (mol-1 dm-3 s-1) Percentage Uncertainty (%)

1 3.5749 x 10-5 ± 13.783

2 6.1345 x 10-5 ± 14.436

3 1.0274 x 10-4 ± 15.367

4 1.6970 x 10-4 ± 15.047

5 2.4709 x 10-4 ± 17.293

19

Now we need to find the values of natural log of k.

Sample Calculation for Trial 1:

= ln (3.5749 × 10−5)

= -10.238999

The absolute uncertainty in a natural log (logarithms to base e, usually written as ln or loge) is equal

to a ratio of the quantity uncertainty and to the quantity12.

Therefore:

ln(𝑘 ± ∆𝑘) = ln(𝑘) ±∆𝑘

𝑘, where

∆𝑘

𝑘 is nothing but the

%𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑘

100

Thus, Percentage uncertainty for ln(𝑘) 𝑖𝑠 ((%𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑘

100) ÷ ln(𝑘)) × 100

For Trial 1, the percentage uncertainty in ln(k) is (13.783

100÷ (−10.238999)) × 100 = ±1.346%

This calculation was done for all the trials. The results are given below:

Table 8.3.9 – Values of Natural Log of rate constant for each trial.

Trial ln(k) Percentage uncertainty (%)

1 -10.2389999 ± 1.346

2 -9.6989891 ± 1.488

3 -9.1832898 ± 1.673

4 -8.6814865 ± 1.733

5 -8.3057410 ± 2.082

12 http://phys114115lab.capuphysics.ca/App%20A%20-%20uncertainties/Print%20AppendixA.htm

20

The activation energy is given by the slope of the graph of ln(𝑘) = −𝐸𝑎

𝑅(

1

𝑇) + ln (𝐴). The plot is

shown below:

Figure 8.3.2 – Arrhenius plot of Iodination of Acetone.

The slope of the graph is -9265.1, which is equal to 𝐸𝑎

𝑅.

−9265.1 =𝐸𝑎

𝑅

𝐸𝑎 = −9265.1 × 𝑅

𝑅 = 8.3144621 𝐽 𝐾−1 𝑚𝑜𝑙−1

Hence,

𝐸𝑎 = −9265.1 × 8.3144621

𝐸𝑎 = −77034.3228 𝐽 𝑚𝑜𝑙−1

𝐸𝑎 = −77.034 𝑘𝐽 𝑚𝑜𝑙−1

The uncertainty in the slope can be calculated by the average of the worst fit lines. One of the worst

fit slopes can be calculated by considering the lowest value possible of the smallest y value and the

highest value possible of the greatest y value, and then calculating the slope of the line joining the

two points.

Least possible y value

−10.238999 − (1.346

100× 10.238999) = −10.376816 Corresponding x = 0.003355705

Greatest possible y value

−8.3057410 + (2.082

100× 8.3057410) = −8.132816 Corresponding x = 0.003144654

y = -9265x + 20.875

-12

-10

-8

-6

-4

-2

0

0.0031 0.00315 0.0032 0.00325 0.0033 0.00335 0.0034

ln(k

) (m

ol-1

dm

3s-1

)

T-1 (K-1)

ln(k) vs T-1

21

𝑆𝑙𝑜𝑝𝑒 = (𝑦2 − 𝑦1)/(𝑥2 − 𝑥1)

𝑆𝑙𝑜𝑝𝑒 = −10.376816 − (−8.132816)

0.003355705 − 0.003144654≈ −10632.5

For the second worst fit slope, we consider the highest value possible of the least y value and the

lowest value possible of the greatest y value.

Highest value of least y value

−10.238999 + (1.346

100× 10.238999) = −10.101182 Corresponding x = 0.003355705

Lowest value of greatest y value

−8.3057410 − (2.082

100× 8.3057410) = −8.378667 Corresponding x = 0.003144654

𝑆𝑙𝑜𝑝𝑒 = −10.101182 − (−8.378667)

0.003355705 − 0.003144654≈ −8161.6

The difference between the actual slope and the worst slopes is as follows:

|−9265.1 − (−10632.5)| = 1367.4

|−9265.1 − (−8161.6)| = 1103.5

Taking the average of the differences gives us the average uncertainty in the slope.

1367.4 + 1103.5

2= 1235.45 ≈ ±1235.5

Therefore, the percentage uncertainty in the slope is

1235.5

9265.1× 100 = 13.33%

The uncertainty in slope is equal to the uncertainty in the value of Activation Energy because ‘R’ is a

constant.

Thus, the Activation Energy of the reaction of Iodination of Acetone is -77.034 ± 13.33% kJ mol-1

22

10 CONCLUSION AND EVALUATION

10.1 EVALUATION From the Graph in Figure 8.3.1, which is a graph of the rate of reaction against temperature, we can

see that according to this graph, there is an exponential increase in the rate with the increase in

temperature. All the values are within the limits of uncertainty, which is increases with the increase

in temperature. This is because these values depend on the standard deviation in the measurements

of time, which stays the same even when the magnitude of time decreases. Thus, the overall

percentage error increases.

The two points marked in red, just touch the trend line with their error bars. The reason for this is

that as the temperature increases, it is difficult to control it using the apparatus set up. When the

temperature becomes greater than 40, the rate of cooling and heating both increases due to the

increase in difference with the room temperature. Therefore, it is difficult to keep the temperature

constant while at lower temperatures, it is not that difficult.

This type of graph also suggests that the reaction follows a general trend seen in most other

reactions, the temperature having a positive and exponential effect on the rate.

The hypothesis during the start of the reaction was that the rate of reaction would increase with the

increase in temperature. This hypothesis is now proven correct by the experiment. This is also

supported by the Boltzmann curve. Increasing the temperature would result in more number of

molecules having enough energy to overcome the activation energy barrier.

Figure 10.1.1 – Effect of increasing temperature on the Boltzmann curve. As the temperature

increases, more number of molecules can overcome the Activation energy barrier and react.13

From the graph in Figure 8.3.2, which is the Arrhenius plot, we can see that all of the points lie on

the trend line. The trend followed by the line is the trend that should be followed for any Arrhenius

plot – a reducing, linear relation.

13 Image source: Pearson Baccalaureate: Higher Level Chemistry for the IB Diploma (Print)

23

10.2 ERROR EVALUATION To render our result in the investigation correct for the activation energy of this reaction, we have

no standard literature value available for comparison. The table below shows the different possible

sources of errors and the effect they could have on the experiment.

Source of Error Type of Error Effect on the Investigation Possible Improvements

Keeping the temperature constant

Systematic The temperature of the reaction mixture was kept constant using heating in a water bath with a Bunsen burner. Whenever the temperature increased, the container was removed from the water bath and whenever the temperature decreased, it was re-immersed. This way, the temperature was not constant throughout a trial. This was a very inefficient way of maintaining a steady temperature, with clear visibility of the contents inside, but with the given limits of apparatus available in the lab, this was the most logical method.

A hot plate with a controlled heating feature can be used. If this is not possible, the experiment can be repeated more number of times and then the values can be averaged. This way, we can get a fairly accurate value.

Presence of water in the beakers

Systematic While making solutions of different concentrations or conducting the reaction, the containers may have some remaining water drops in them due to a previous wash. This way, there might be small variations in the concentration, or presence of impurities in the reaction which could have an effect in the rate.

The beakers or the other containers can be washed and dried by a dry cloth which would absorb the water. Also, acetone can be used to wash the beaker, as acetone would then evaporate from the beaker, leaving it completely dry.

Variation in pressure Systematic The pressure in the reaction container during the experiment could vary each time, because the container was closed with a cork, to prevent evaporation of acetone. Consequently, the pressure might have also changed in the container, causing a change in the rate of reaction.

Using larger container, change in pressure is minimum.

24

Watching colour change

Systematic The colour change was identified visually. This may have some error in terms of timely identification. Due to external light, it was difficult to identify the colour change. This might have caused an error in the reading of the time.

A light sensor apparatus can be made, which uses the principle of colorimeter. Electronically viewing the colours would decrease the chances of error.

11 FURTHER INVESTIGATION

The investigation can be taken further by finding the Activation energy of different compounds when

reacted with Iodine, for example, the Iodination of Ethanol. This way, the Activation Energy of

different organic compounds when reacted with Iodine can be compared. Furthermore, other

Arrhenius parameters for this reaction can also be studied, like the frequency factor. The frequency

factor of the reaction can be calculated from the y-intercept of the Arrhenius plot. The Frequency

Factor of different reactions can also be studied and compared. From this analysis, we can get to

know how readily a reaction takes place in contrast with others. A reaction with high Frequency

Factor would have a lesser Activation energy requirement, and vice versa. Along with this, the

results of the same experiment could be compared by using different methods. For instance,

spectrometry can be used to observe the rate of change of concentration of the reactants, and then

determine the Activation Energy.

25

12 BIBLIOGRAPHY

MHChem

http://mhchem.org/222/pdfLabs222/KineticsPartI.pdf

Clark University

http://web.clark.edu/amixon/142_pm/w10kinetics.pdf

ChemWiki

http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Modeling_Reaction_Kinetics/Temperatur

e_Dependence_of_Reaction_Rates/The_Arrhenius_Law/The_Arrhenius_Law%3A_Activation_Energi

es

Dr. Paul J. McElligott

http://www.pjmcelligottcom.com/152LLProject1-Kinetics.pdf

Charleston Country School District

http://amhs.ccsdschools.com/common/pages/DisplayFile.aspx?itemId=11411346